A Linear Relation between the Color Stretch sBV and the Rising Color Slope s0*(B−V) of Type Ia Supernovae

Using data from the Complete Nearby (redshift z_host < 0.02) sample of Type Ia Supernovae (CNIa0.02), we find a linear relation between two parameters derived from the B − V color curves of Type Ia supernovae: the color stretch sBV and the rising color slope  after the peak, and this relation applies to the full range of sBV. The sBV parameter is known to be tightly correlated with the peak luminosity, especially for fast decliners (dim Type Ia supernovae), and the luminosity correlation with sBV is markedly better than with the classic light-curve width parameters such as Δm₁₅(B). Thus, our new linear relation can be used to infer peak luminosity from . Unlike sBV (or Δm₁₅(B)), the measurement of  does not rely on a well-determined time of light-curve peak or color maximum, making it less demanding on the light-curve coverage than past approaches.